Solving Linear Equations - Review Lecture

Key Concepts

• Solving Linear Equations: Involves simplifying both sides of the equation, then isolating the variable to find its value.
• Distributive Property: Used to simplify expressions by distributing a multiplier across terms inside parentheses.
• Combining Like Terms: Essential step in simplifying expressions.

Example 1

Steps:

1. Distribute:
   • Left: Distribute the 3 across terms: (3(x - 2) + 7)
   • Right: Distribute the 2: (2(x + 5))
2. Simplify:
   • Left: Combine like terms: (3x - 6 + 7 = 3x + 1)
   • Right: No like terms to combine, (2x + 10)
3. Isolate X:
   • Subtract 2x from both sides: (3x - 2x + 1 = 2x - 2x + 10)
   • Simplify: (x + 1 = 10)
4. Solve for X:
   • Subtract 1 from both sides: (x = 9)
   • Solution: When (x = 9), the equation holds true.

Example 2 - Fractions

Approach:

1. Fractions: Convert whole numbers to fractions by placing them over 1.
2. Common Denominator:
   • Find a common denominator for all terms, e.g., 8.
3. Rewrite Expressions:
   • Convert each fraction to have the common denominator.
4. Solve:
   • Focus on numerators after common denominators are applied.
   • Solve like a regular linear equation.

Example 3

Steps:

1. Common Denominator:
   • Multiply denominators to find a common one, e.g., 28.
2. Rewrite Terms:
   • Ensure each term has the common denominator.
3. Simplify:
   • Remove denominators and simplify the equation.
4. Solve for X:
   • Combine like terms and solve for the variable.

Example 4 - Multiple Terms in Numerator

Tips:

1. Parentheses:
   • Use parentheses to handle multiple terms in the numerator.
2. Common Denominator:
   • Find a common denominator for all terms.
3. Distribution:
   • Distribute terms within parentheses and simplify.
4. Final Steps:
   • Isolate X and solve.

Conclusion

• Practice: Practice solving various types of equations to strengthen understanding.
• Next Steps: Prepare for more complex equations in upcoming lessons.